Nonlinear dynamical processes and interactions influence a wide variety of physical systems of fundamental and applied significance. Nonlinear dynamical systems appear in physics, chemistry, engineering, biology, and economics, among other disciplines, representing such diverse phenomena as soliton generation in Bose-Einstein condensates, chemical oxidation processes, complex vibrations in engineering structures, biochemical processes in cell cycle initiation, traffic pattern evolution, climate changes, and social interactions. Specific examples of industrial importance include nonlinear MEMS devices of various geometries, which are widely used for applications ranging from accelerometers to stress sensors; nonlinear circuit components, which provide advantages over traditional ohmic circuits by providing enhanced sensitivity in certain applications and play a pivotal role in semiconductor devices; and atomic force microscopy, which has recently become a popular tool for characterizing the mechanical properties of materials via nonlinear interaction forces.
Measuring and assessing the parameters governing the dynamics of such generally nonlinear systems is thus of critical importance for both fundamental investigations and industrial applications. However, the nonlinearity makes characterizing the properties of these systems difficult, and no general method of measurement and assessment of dynamical nonlinear systems is known to have previously existed. The present method and apparatus disclosed herein assesses the effective dynamical properties for a large class of nonlinear systems.